You can use the .slice method:
var old = ["Apples", "Bananas"];
var newArr = old.slice(0);
newArr.reverse();
// now newArr is ["Bananas", "Apples"] and old is ["Apples", "Bananas"]
Array.prototype.slice returns a shallow copy of a portion of an array. Giving it 0 as the first parameter means you are returning a copy of all the elements (starting at index 0 that is)